Problem 6.1 is a practice problem for similar triangles but also a warm-up for 6.2. Problem 6.2 is a very important result that on Monday we will discuss in depth.
Problem 6.3 is a tougher exercise in ratios. You will need to know how to do these, but if you get stuck this first time, don't worry. We will present some strategies for organizing such problems next week that may make it seem simpler afterwards.
Let ABC be an isosceles triangle with AB = AC. Let D be a point on AB with CD = CB. If |AB| = 63 and |BC| = 17, what is |BD|? Show your reasoning
Let ABC be an isosceles triangle with AB = AC. Let D be a point on AB. In this triangle AC = AB = d and CB = CD = DA = s.
a) Find an equation relating d and s.
b) If angle BAC = x, find (if possible) the measures of all other angles in the figure in terms of x.
c) Examine the angle measures and their relationship to find (if possible) the value of x and the measure of all the angles.
d) Is the ratio d/s determined to be a particular fixed number by the relationships in the figure? Solve (if possible), your equation in (a) for d/s. Hint: If you have trouble with this, tell what you can say about d, when s = 1.
Given triangle ABC with points E on AC and D on
Suppose that DE is parallel to BC and AE/AC = 7/13. Find exact rational numbers that answer the following questions. Show your reasoning. (You can also find decimal approximations and check your work with Sketchpad.)
a) What is the ratio BF/FE?
b) What is the ratio BF/BE?
c) What is the ratio AF/AG?